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Mirrors > Home > ILE Home > Th. List > Mathboxes > bdop | Unicode version |
Description: The ordered pair of two setvars is a bounded class. (Contributed by BJ, 21-Nov-2019.) |
Ref | Expression |
---|---|
bdop | BOUNDED |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bdvsn 9994 | . . . 4 BOUNDED | |
2 | bdcpr 9991 | . . . . . . 7 BOUNDED | |
3 | 2 | bdss 9984 | . . . . . 6 BOUNDED |
4 | ax-bdel 9941 | . . . . . . . 8 BOUNDED | |
5 | ax-bdel 9941 | . . . . . . . 8 BOUNDED | |
6 | 4, 5 | ax-bdan 9935 | . . . . . . 7 BOUNDED |
7 | vex 2560 | . . . . . . . . . . 11 | |
8 | 7 | prid1 3476 | . . . . . . . . . 10 |
9 | ssel 2939 | . . . . . . . . . 10 | |
10 | 8, 9 | mpi 15 | . . . . . . . . 9 |
11 | vex 2560 | . . . . . . . . . . 11 | |
12 | 11 | prid2 3477 | . . . . . . . . . 10 |
13 | ssel 2939 | . . . . . . . . . 10 | |
14 | 12, 13 | mpi 15 | . . . . . . . . 9 |
15 | 10, 14 | jca 290 | . . . . . . . 8 |
16 | prssi 3522 | . . . . . . . 8 | |
17 | 15, 16 | impbii 117 | . . . . . . 7 |
18 | 6, 17 | bd0r 9945 | . . . . . 6 BOUNDED |
19 | 3, 18 | ax-bdan 9935 | . . . . 5 BOUNDED |
20 | eqss 2960 | . . . . 5 | |
21 | 19, 20 | bd0r 9945 | . . . 4 BOUNDED |
22 | 1, 21 | ax-bdor 9936 | . . 3 BOUNDED |
23 | vex 2560 | . . . 4 | |
24 | 23, 7, 11 | elop 3968 | . . 3 |
25 | 22, 24 | bd0r 9945 | . 2 BOUNDED |
26 | 25 | bdelir 9967 | 1 BOUNDED |
Colors of variables: wff set class |
Syntax hints: wa 97 wo 629 wceq 1243 wcel 1393 wss 2917 csn 3375 cpr 3376 cop 3378 BOUNDED wbdc 9960 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-bd0 9933 ax-bdan 9935 ax-bdor 9936 ax-bdal 9938 ax-bdeq 9940 ax-bdel 9941 ax-bdsb 9942 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ral 2311 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-sn 3381 df-pr 3382 df-op 3384 df-bdc 9961 |
This theorem is referenced by: (None) |
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